The Representation of Homeomorphisms on the Interval as Finite Compositions of Involutions
Sam W. Young · Proceedings of the American Mathematical Society · 1994
It is known that every homeomorphism on the interval is the composition of at most four involutions and that every decreasing homeomorphism is the composition of at most three involutions. We will characterize those homeomorphisms that are the composition of two involutions. It is then demonstrated that there exist three involutions that together generate a dense subgroup of the topological group of all homeomorphisms on the interval.